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It is well known that the sum of the primitive roots modulo $p$ is congruent to $\mu(p − 1) \bmod{p}$.

But I can't see why this result is interesting or useful. Can someone please enlighten me?

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Related:… – JavaMan Jan 12 '12 at 16:08
@JavaMan, thanks, I've seen this and I have added my question there as a comment but I though an actual question would be more visible. Moreover, that question you mentioned does not touch my question. – lhf Jan 12 '12 at 16:11
After I included the link, I saw that you commented there. I wasn't sure whether to keep the link here or not, but I agree that asking this as a new question will attract more attention. – JavaMan Jan 12 '12 at 16:47
Is there a reason to think that it is particularly interesting or useful? I'm not saying it's not, but it looks like a homework problem relating a cute fact you get by looking at coefficients of minimal polynomials... – Cam McLeman Jan 12 '12 at 17:11
It can never be a bad idea to look at the Disquisitiones. – Gerry Myerson Jan 25 '12 at 1:35

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